Question

Rezolvati ecuatiile:
a) |x-2| =3;
b) ||x-2|-2|=3;
c) |||x-2|-2|-2|=3.
Mulţumesc!

Answer 1

a) x-2=3 sau x-2=-3
x-2=3; x=3+2; x=5;
x-2=-3; x=-3+2; x=-1
S={-1, 5}

b) |x-2|-2=3 sau |x-2|-2=-3
|x-2|-2=3; |x-2|=3+2; |x-2|=5 
|x-2|-2=-3; |x-2|=-3+2; |x-2|=-1 nu se poate
Deci x-2=5 sau x-2=-5
x-2=5; x=2+5; x=7;
x-2=-5; x=-5+2; x=-3
S={-3, 7}

c) |||x-2|-2|-2=3 sau |||x-2|-2|-2=-3

|||x-2|-2|-2=3; ||x-2|-2|=3+2; |||x-2|-2|=5
|||x-2|-2|-2=-3; ||x-2|-2|=-3+2; ||x-2|-2|=-1 Nu se poate
|x-2|-2=5 sau |x-2|-2=-5
|x-2|-2=5; |x-2|=5+2; |x-2|=7
|x-2|-2=-5; |x-2|=-5+2; |x-2|=-3; Nu se poate
x-2=7 sau x-2=-7
x-2=7; x=7+2; x=9;
x-2=-7; x=-7+2; x=-5;

|||x-2|-2|-2=-3; |||x-2|-2|=-3+2; |||x-2|-2|=-1 Nu se poate

S={-5, 9}